Frequency characterization of a thin linear antenna using diakoptic antenna theory

A frequency-dependent analytical expression for the input impedance of a thin wire antenna is obtained using diakoptic theory. The linear antenna is diakopted into electrically short segments, where each is treated as a component with two terminals (except for end pieces, which have only one terminal). An impedance matrix is found which characterizes coupling between all segments. By expanding the free-space Green´s function in a power series in wavenumber k, each entry in the resultant impedance matrix is obtained as an explicit function of frequency. The input admittance is found as a ratio of two polynomials in wavenumber k. A more systematic approach for the solution of the input admittance is achieved by expanding both the unknown current vector and the Green´s function in power series in k. Equating coefficients of like powers in k leads to a numerically efficient algorithm which is used to determine the input admittance as a function of frequency. Numerical results compare well with the input impedance obtained from a conventional integral equation solution